Some great analysis here. Sorry to get off track, but something occurred to me after reading this.

So far it seems we are assuming that the Federation is only lost territory/space/planets to the Klingons through capture and occupation. I think it is important to consider that possibility that some of the planets or members of the Federation defected to the Klingons. War is arguably just as much about cutting off the enemy's supply lines as it is about battle tactics and firepower. I see no reason this couldn't hold true here.

We know from the Genesis Proposal in TWOK that the federation anticipated difficulty meeting the needs for a growing population. Since Genesis failed, it is likely that this would have become a problem, if it wasn't already. And entering into a full scale war would further tax resources.

We have seen the Klingons attempt to "court" planets that the Federation was attempting to negotiate mining rights with in TOS: Friday's Child. Once the Federation is unable to dedicate as many resources to support their colonies and members as a result of war, Klingons could quickly step in and offer compelling reasons for them to switch sides. Though the Klingons may not be as resource rich, they are very permissible to things that the Federation forbids. Such as the use of Orion slaves. Though abhorrent, if a colony is short on resources and faces starvation, the possibility of using slave labor to mine resources for trade and build infrastructure would start to become compelling.

Adding to the already scaled back military from the Khitomer Accords, the loss of resources from these worlds would put further strain on Federation, forming a vicious cycle. Ultimately, the loss of many of their supporters is what pushes the Federation into a losing position.

Of course, this basically goes against the assertions that there is no scarcity or poverty in the 24th century. But even if we assume this is true on the key federation worlds like Earth, I really can't see this being the case for every single federation colony and outpost. Of course, if we assume that the materials used to produce a starship can all be replicated, then its not really clear what other resources might be needed beside the dilithium crystals, antimater (however the heck that stuff is being made or collected) and trained bodies to crew the ships.